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A201490 Number of nX2 zero-sum -2..2 arrays with rows and columns lexicographically nondecreasing.

%I A201490 #7 Jul 22 2025 16:16:07
%S A201490 3,29,226,1454,7815,36487,151593,571539,1982705,6399842,19389074,
%T A201490 55531190,151238480,393631919,983211316,2365399764,5498241469,
%U A201490 12382111994,27080912704,57644263473,119645822176,242563511707
%N A201490 Number of nX2 zero-sum -2..2 arrays with rows and columns lexicographically nondecreasing.
%C A201490 Column 2 of A201496
%H A201490 R. H., <a href="/A201490/b201490.txt">Table of n, a(n) for n = 1..210</a>
%F A201490 Empirical: a(n) = 6*a(n-2) +7*a(n-3) -10*a(n-4) -38*a(n-5) -31*a(n-6) +48*a(n-7) +148*a(n-8) +133*a(n-9) -96*a(n-10) -416*a(n-11) -479*a(n-12) -12*a(n-13) +797*a(n-14) +1265*a(n-15) +706*a(n-16) -835*a(n-17) -2315*a(n-18) -2338*a(n-19) -344*a(n-20) +2577*a(n-21) +4244*a(n-22) +3040*a(n-23) -620*a(n-24) -4336*a(n-25) -5478*a(n-26) -3214*a(n-27) +932*a(n-28) +4370*a(n-29) +5360*a(n-30) +3926*a(n-31) +1155*a(n-32) -1908*a(n-33) -4647*a(n-34) -6321*a(n-35) -5666*a(n-36) -1759*a(n-37) +4482*a(n-38) +9788*a(n-39) +10241*a(n-40) +4382*a(n-41) -4896*a(n-42) -11847*a(n-43) -11847*a(n-44) -4896*a(n-45) +4382*a(n-46) +10241*a(n-47) +9788*a(n-48) +4482*a(n-49) -1759*a(n-50) -5666*a(n-51) -6321*a(n-52) -4647*a(n-53) -1908*a(n-54) +1155*a(n-55) +3926*a(n-56) +5360*a(n-57) +4370*a(n-58) +932*a(n-59) -3214*a(n-60) -5478*a(n-61) -4336*a(n-62) -620*a(n-63) +3040*a(n-64) +4244*a(n-65) +2577*a(n-66) -344*a(n-67) -2338*a(n-68) -2315*a(n-69) -835*a(n-70) +706*a(n-71) +1265*a(n-72) +797*a(n-73) -12*a(n-74) -479*a(n-75) -416*a(n-76) -96*a(n-77) +133*a(n-78) +148*a(n-79) +48*a(n-80) -31*a(n-81) -38*a(n-82) -10*a(n-83) +7*a(n-84) +6*a(n-85) -a(n-87)
%e A201490 Some solutions for n=6
%e A201490 .-2..1...-2.-2...-2.-2...-2..1...-2.-2...-1..0...-2.-2...-2..0...-2.-1...-2..2
%e A201490 .-1..2...-1..0...-1..1...-2..2...-1..1....0.-1...-2..1....0.-2...-2..1...-1.-1
%e A201490 ..0.-1...-1..1....0.-2...-1.-1....0..2....0.-1...-2..2....0..0....1.-2....0..1
%e A201490 ..0..0....1..0....0..0....1.-1....1.-2....1..1....1..0....0..0....1..1....1.-2
%e A201490 ..1.-2....1..0....2..0....1.-1....1..0....2.-2....2.-1....1..2....1..1....1..0
%e A201490 ..1..1....2..1....2..2....2..1....2..0....2.-1....2..1....2.-1....2.-1....1..0
%K A201490 nonn
%O A201490 1,1
%A A201490 _R. H. Hardin_ Dec 02 2011